Helioseismic Diagnostics of Solar Convection and Activity PDF
Preview Helioseismic Diagnostics of Solar Convection and Activity
HELIOSEISMIC DIAGNOSTICS OF SOLAR CONVECTION AND ACTIVITY Edited lJy THOMAS L. DUVALL, le. NASA Goddard Space FUg/II Cemer JOHN W. HARVEY NmÎonal Solar ObservQlOry National Optica' ASlrallom)' Observatory, Tucsoll ALEXANDER G. KOSOVICHEV Stanford Universiry, Stanford ZDENEK SVESTKA CASS UCSD al/d SRON V1recll, Rcprintcd from SO/lIr Php in . Volume 192. Nos. 1-2. 200ll and Volume 193. Nos. 1-2.2000 .. SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-94-010-5882-7 ISBN 978-94-011-4377-6 (eBook) DOI 10.1007/978-94-011-4377-6 Printed an acid-free paper AH Rights Reserved ©200 1 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint ofthe hardcover Ist edition 2001 No part of the material protected by this copyright notice may be reproduced or utilized in any form ar by any means, electronic or mechanical, including photocopying, recording ar by any information starage and retrieval system, without written permission from the copyright owner. TABLE OF CONTENTS PREFACE 1-2 I. THEORIES OF SOLAR CONVECTION, ROTATION, AND ACTIVITY DOUGLAS GOUGH / Towards Understanding Solar Convection and Activity 3-26 PETER A. GILMAN / Fluid Dynamics and MHD of the Solar Convection Zone and Tachocline: Current Understanding and Unsolved Problems 27-48 ALEXANDER RUZMAIKIN / Can We Get the Bottom B? 49-57 MARK S. MIESCH / The Coupling of Solar Convection and Rotation 59-89 ROBERT F. STEIN and A.KE NORDLUND / Realistic Solar Convection Simulations 91-108 N. E. HURLBURT, P. C. MATTHEWS and A. M. RUCKLIDGE / Solar Magnetoconvection 109-118 G. H. FISHER, Y. FAN, D. W. LONGCOPE, M. G. LINTON and A. A. PEVTSOV / The Solar Dynamo and Emerging Flux 119-139 Y. FAN and DONGLAI GONG / On the Twist of Emerging Flux Loops in the Solar Convection Zone 141-157 II. HELIOSEISMIC TOMOGRAPHY A. G. KOSOVICHEV, T. L. DUVALL JR. and P. H. SCHERRER / Time-Distance Inversion Methods and Results 159-176 T. L. DUVALL JR. and L. GIZON / Time-Distance Helioseismology with f Modes as a Method for Measurement of Near-Surface Flows 177-191 A. C. BIRCH and A. G. KOSOVICHEV / Travel Time Sensitivity Kernels 193-201 1. E. RICKETT and J. F. CLAERBOUT / Calculation of the Sun's Acoustic Impulse Response by Multi-Dimensional Spectral Factorization 203-210 GARY H. PRICE / Ray Travel Time and Distance for the Planar Poly trope 211-223 MARCUS BRUGGEN / The Parabolic Wave Equation in Local Helioseismology 225-230 JESPER MUNK JENSEN, BO HOLM JACOBSEN and J0RGEN CHRISTENSEN- DALSGAARD / Sensitivity Kernels for Time-Distance Inversion 231-239 Ill. ACOUSTIC IMAGING AND HOLOGRAPHY DEAN-YI CHOU / Acoustic Imaging of Solar Active Regions 241-259 C. LINDSEY and D. C. BRAUN / Basic Principles of Solar Acoustic Holography 261-284 D. C. BRAUN and C. LINDSEY / Helioseismic Holography of Active-Region Subphotospheres 285-305 D. C. BRAUN and C. Lindsey / Phase-Sensitive Holography of Solar Activity 307-319 A.-C. DONEA, C. LINDSEY and D. C. BRAUN / Stochastic Seismic Emission from Acoustic Glories and the Quiet Sun 321-333 IV. RING-DIAGRAM ANALYSIS D. A. HABER, B. W. HINDMAN, 1. TOOMRE, R. S. BOGART, M. J. THOMPSON and F. HILL / Solar Shear Flow Deduced from Helioseismic Dense-Pack Samplings of Ring Diagrams 335-350 IV TABLE OF CONTENTS MARC DE ROSA, T. L. DUVALL JR. and JURI TOOMRE I Near-Surface Flow Fields Deduced Using Correlation Tracking and Time-Distance Analyses 351-361 BRADLEY HINDMAN, DEBORAH HABER, JURI TOOMRE and RICK BOGART I Local Fractional Frequency Shifts Used as Tracers of Magnetic Activity 363-372 V. MAGNETIC FIELDS AND OSCILLATIONS T. J. BOGDAN I Sunspot Oscillations: A Review 373-394 P. S. CALLY / Modelling p-Mode Interaction with a Spreading Sunspot Field 395-401 A. A. NORTON and R. K. ULRICH I Measuring Magnetic Oscillations in the Solar Photosphere: Coordinated Observations with MDI, ASP and MWO 403-413 JUN ZHANG, JINGXIU WANG, CHIK-YIN LEE and HAIMIN WANG I Interaction between Network and Intranetwork Magnetic Fields 415-426 VI. SOLAR-CYCLE VARIATIONS OF THE INTERNAL STRUCTURE AND ROTATION R. HOWE, R. KOMM and F. HILL I Variations in Solar Sub-Surface Rotation from GONG Data 1995-1998 427-435 J. TOOMRE, J. CHRISTENSEN-DALSGAARD, R. HOWE, R. M. LARSEN, J. SCHOU and M. J. THOMPSON / Time Variability of Rotation in Sol ar Convection Zone from SOI-MDI 437-448 SARBANI BASU and H. M. ANTIA / Possible Solar Cycle Variations in the Convec tion Zone 449-458 H. M. ANTIA, SARBANI BASU, J. PINTAR and B. POHL I Solar Cycle Variation in Solar f-Mode Frequencies and Radius 459-468 SARBANI BASU and H. M. ANTIA / Solar Cycle Variations of Large-Scale Flows in the Sun 469-480 SARBANI BASU and JESPER SCHOU / Does the Tachocline Show Solar Cycle Related Changes? 481-486 KIRAN JAIN, S. C. TRIPATHY, A. BHATNAGAR and BRAJESH KUMAR / Empir ical Estimate of p-Mode Frequency Shift for Solar Cycle 23 487-494 VIT. SOLAR CONVECTIVE STRUCTURES AND OSCILLATIONS D.H. HATHAWAY, J.G. BECK, R.S. BOGART, K.T. BACHMANN, G. KHATRI, J.M. PETITTO, S. HAN and J. RAYMOND I The Photospheric Convection Spectrum 495-508 R.A. SHINE, G.w. SIMON and N.E. HURLBURT / Supergranule and Mesogranule Evolution 509-527 JOHN G. BECK and JESPER SCHOU I Supergranulation Rotation 529-539 M.C. RABELLO-SOARES, SARBANI BASU, J. CHRISTENSEN-DALSGAARD and M.P. DI MAURO I The Potential of Solar High-Degree Modes for Struc ture Inversion 541-552 CHIA-HSIEN LIN and WERNER DApPEN / Investigating the Excitation of Acoustic Modes Using Homomorphic Deconvolution 553-560 ANTONIO EFF-DARWICH and SYLVAIN G. KORZENNIK / Response of the Radial Stratification at the Base of the Convection Zone to the Activity Cycle 561-567 G. BARNES and P.S. CALLY / Mode Mixing by a Shallow Sunspot 569-578 PREFACE Most papers in this book were presented at the SOHO-9 Workshop 'Helioseismic Diagnostics of Solar Convection and Activity', held on 12-15 July 1999 at Stanford University, California, U.S.A. Some papers which were not presented at the work shop have been added, after authors had been invited in Solar News to contribute to this book. All papers submitted to this book have been refereed, and only those of high scientific quality were accepted for publication. The book focuses on the recent advances in our understanding of solar con vection and activity, and on methods and results of helioseismic diagnostics of the internal structures and dynamics of solar convection and active regions. The methods of local helioseismology (time-distance tomography, ring-diagram analy sis, acoustic imaging and holography), intensively developed in the past few years, have provided promising results on the deep structure of large-scale convection and flows, emerging active regions, and sunspots. Along with the traditional 'global' helioseismology based on frequencies of resonant oscillation modes, the local-area techniques have become increasingly important for studying the solar interior and the mechanisms of solar activity. The new high-resolution helioseismology projects 'Solar Oscillation Investiga tionlMichelson Doppler Imager' (SOIlMDI) on board SOHO, and ground-based 'Global Oscillation Network Group' (GONG) have provided a tremendous amount of solar oscillation data. Extracting from these data the information about the in ternal properties and dynamics of the Sun, and using this information in theoretical models and space weather forecasts are new challenges in solar physics. This book consists of both invited reviews and contributed papers divided into seven sections: 1. Theories of Solar Convection, Rotation and Activity. 2. Helioseismic Tomography. 3. Acoustic Imaging and Holography. 4. Ring-Diagram Analysis. 5. Magnetic Fields and Oscillations. 6. Solar-Cycle Variations of the Internal Structure and Rotation. 7. Solar Convective Structures and Oscillations. Of course, this division is rather conditional because some papers cover several of these SUbtopics. However, we believe that this will guide the reader through the book. 2 We hope that this book will stimulate further development of the helioseismic diagnostics and theoretical modeling of the physical processes inside the Sun. ALEXANDER G. KOSOVICHEV THOMAS L. DUVALL, Jr. TOWARDS UNDERSTANDING SOLAR CONVECTION AND ACTIVITY (Invited Review) DOUGLAS GOUGH Institute ofA stronomy, Madingley Road, Cambridge, CB3 OHA, U.K.; Dept Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB39EW, U.K.; J1LA, Campus Box 440, University of Colorado, Boulder, CO 80309-0440, U.S.A.; Dept Physics, HEPLAnnex B206, Via Palau, Stanford, CA 94305-4085, U.S.A. (Received 5 October 1999; accepted 16 February 2000) Abstract. The dynamics of the large-scale eddies which advect angular momentum through the convection zone is controlled in a significant way by the boundary conditions, which, if they are not modelled adequately, do not lead to a distribution of angular velocity that is consistent with observation. The transition boundary layer separating the convection zone from the radiative interior is thought to play a critical role in controlling the magnetic field in the convection zone, and is probably not wholly irrelevant to understanding the cycle of solar activity. 1. Introduction Understanding is familiarity: to understand something new is to think of it in terms of concepts that one commonly encounters - to relate it to phenomena that one experiences often and with which one feels intellectually comfortable. Evidently, the direction in which one heads in order to approach understanding depends on one's prior knowledge, on one's educational and developmental background, which itself depends, to some degree, on how the subject under consideration has de veloped. It is with this in mind that I direct my discussion, hoping that there is sufficient overlap of our domains of familiarity for something useful to emerge. I cannot attempt to explain the many interesting properties of the Sun that have been discussed at this meeting. Instead, I mainly raise issues that are related to them; it is my hope that by so doing the direction in which we might head to acquire the understanding we seek will become more evident. 2. Some Comments on Solar Convection A common approach to understanding convection is to think in terms of the energy spectrum. At the most basic level, one can divide the spectral range into three, as in Figure 1, in which energy density 8 is plotted logarithmically against characteristic wave number: there is a range A encompassing the energy-density maximum, a global range B of scales larger than those of A, and a range C of smaller scales. It Helioseismic diagnostics of solar convection and activity. Reprinted from Solar Physics 192, 2000. © Kluwer Academic Publishers. 4 D.GOUGH log k Figure 1. Cartoon of the energy-density spectrum of turbulent convection. is common practice to divide range C into two subranges, one of relatively large scales in which dissipation is negligible, the other in which the dissipation is all important; but since, as I shall argue later, it seems unlikely that the dissipative range plays an important role in influencing the global dynamics of convection, I shall not do so. The objective now is to understand at a phenomenological level how motions in these three regions influence each other. The eddies of A are driven by buoyancy, extracting their kinetic energy from the potential energy of the unstable stratification of the Sun's convective envelope. As a direct consequence of this energy conversion, there must necessarily be, on the whole, a positive correlation between positive/negative temperature fluctuations and upwardly/downwardly directed motion. Therefore, there is a positive (upward) convective heat flux (enthalpy flux). The correlation between kinetic energy density 1Pu . u and the vertical component of the turbulent velocity u is not so great. Nevertheless, it is not negligible, and it does contribute substantially to the total flux of energy through the convection zone. I shall not address that flux here, however, for my main interest is in the turbulent Reynolds stresses Rij = PUi U j (in Cartesian suffix notation, and where the overbar denotes ensemble average) which cause, in particular, angular momentum to be transported on the larger scale B and thereby influence the variation of the Sun's angular velocity. The reason to be interested in that is firstly that rotational shear is bound to have a major influence on the intensification and transport of the large-scale magnetic field, which is one of the principle interests of this conference, and secondly that angular velocity is one of the solar properties that can be measured directly by seismological analysis. That TOWARDS UNDERSTANDING SOLAR CONVECTION AND ACTIVITY 5 is not to say that the kinetic-energy flux plays no role in the global (rotational) dynamics of the convection zone. It is simply that the role of that flux is probably of secondary importance. Moreover, so far as I am aware, it is very poorly understood in that context, if at all. That the eddies of region A should not be isotropic is obvious, and has been known for a long time. Firstly, they are driven by an anisotropic force, namely buoyancy, which is vertically directed, and secondly, because they are in a rotating environment, they are influenced by a Coriolis force, which is essentially perpen dicular to the vorticity of the large-scale flow of the spectral range B. The latter is true particularly of the large eddies deep in the convection zone whose vorticity is comparable with the vorticity associated with the solar rotation. The smaller granulation near the surface of the Sun, which appears to be buoyancy driven and therefore belongs to range A, has a much higher vorticity, and its dynamics is accordingly influenced less. However, as we shall see later, that influence is probably not negligible. Given that the eddies of range A are anisotropic, so also must be their con tribution to Rij. Consequently, we know at the outset that the effect of turbulent momentum transport across a shear cannot be the same as that due to a scalar viscosity. Some years ago I tried to take steps to formulate a description of eddy dynamics - basically a mixing-length theory - to take Coriolis effects into account in the estimation of Rij (Gough, 1978), and soon afterwards Durney and Spruit (1979) made a similar attempt from a rather different standpoint. Neither approach has been extensively pursued and tested, and many people doubt that it would be worthwhile. That may be so, and the opinion is understandable because mixing length theory, particularly as it is used in stars, is not even self-consistent. But, until today at least, there has been no alternative to mixing-length theory for stellar modelling, and so solar and stellar physicists have continued to use it. There is always hope that the theory could be calibrated in some way to render it useful under limited circumstances, and indeed for the purpose of studying the mean hydrostatic stratification of the Sun there is evidence that the theory does have some utility. There is additional evidence from studies of the excitation and damping of solar oscillations; I shall return to that topic later. But here I register my surprise not just at the extensive, almost universal use of a scalar turbulent eddy diffusivity to describe how heat and momentum are transported, but at the degree of credulity with which the executors proffer the results of so doing. A notable exception, for steady states, is given to us by Rudiger (1989) and his collaborators, who have developed a more plausible approach to describing anisotropic stress, and who have investigated the implications of this approach concerning the global dynamics of statistically steady solar convection. I shall address time dependence later. I must at this point point out that the very impressive calculations presented to us by Stein and Nordlund (2000) do give us hope for substantial improvement in convective modelling in the future. We know (from mixing-length theory, and similar scaling arguments) that, aside from in the uppermost layers, the convection
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